Jieqing Feng

Curvature estimation of point-sampled surfaces and its applications

In this paper, we propose a new approach to estimate curvature information of point-sampled surfaces. We estimate curvatures in terms of the extremal points of a one-dimensional energy function for discrete surfels (points equipped with normals) and a multi-dimensional energy function for discrete unstructured point clouds. Experimental results indicate that our approaches can estimate curvatures faithfully, and reflect the subtle curvature variations. Some applications for curvature information, such as surface simplification and feature extraction for point-sampled surfaces, are given.

Arc-length-based axial deformation and length preserved animation

In real life, some objects may deform along axial curves and the lengths of their skeletons usually remain constant during the axial deformation, such as a swimming fish, a swaying tree, etc. This paper presents a practical approach of arc-length-based axial deformation and axial-length-preserved animation. The space spanned by the arc-length parameter and the rotation-minimizing frame on the axis is taken as the embedding space. During animation, the keyframe axial curves are consistently approximated by polylines after sufficient subdivisions and both the edge lengths and the directional vertex angles of the keyframe polylines (or unit edge vectors) are then interpolated to generate the intermediate polylines which are regarded as the discrete expressions of the intermediate axes. Experiments show that our method is very useful, intuitive and easy to control.

Free-form deformation with automatically generated multiresolution lattices

Developing intuitive and efficient methods for shape editing is one of the most important areas in computer graphics, and free-form deformation (FFD), which is one of such methods, allows the user to deform a model easily by moving a set of control points, collectively called the lattice. Although the FFD method can be used for both global and local deformations, the user must define a suitable lattice manually or use a simple shaped lattice such as a parallelepiped. Therefore, we propose a new FFD method that automatically generates the lattices with which both types of deformations can be achieved. Our method refines a bounding box of the model and generates a set of finer lattices, which hierarchically approximate the shape of the model. Through adjusting the control points of the generated lattices, both global and local deformations of the model can be achieved easily. Moreover, the method allows hierarchical deformation of the model by combining different levels of lattice.

Bézier surfaces of minimal internal energy

In this paper the variational problems of finding Bezier surfaces that minimize the bending energy functional with prescribed border for both cases of triangular and rectangular are investigated. As a result, two new bending energy masks for finding Bezier surfaces of minimal bending energy for both triangular and rectangular cases are proposed. Experimental comparisons of these two new bending energy masks with existing Dirichlet, Laplacian, harmonic and average masks are performed which show that bending energy masks are among the best.

B-spline free-form deformation of polygonal objects through fast functional composition

Free-form deformation, abbreviated to FFD, plays an important role in both computer animation and geometric modeling. When polygonal objects are deformed by the traditional FFD scheme, however aliasing will appear since the deformation only acts on the sample points of the objects. To eliminate this problem, a new method of accurate B-spline FFD was proposed by authors previously, which is based on functional composition. Unfortunately it is a time consuming process because generalized de Casteljau algorithm is adopted to solve the functional composition. In this paper we propose a fast accurate B-spline FFD method. The proposed method makes use of the polynomial interpolation and symbolic computation to solve the functional composition. Both theoretical analysis and implementation results show that the proposed method runs faster than the original one.

Detail-Preserving local editing for point-sampled geometry

In digital geometry processing, it is important to preserve the intrinsic properties of 3D models in geometry editing operations. One of such intrinsic properties can be described as geometric details. For point-sampled geometry, combining the Normal Geometric Details (NGDs) and the Position Geometric Details (PGDs), a useful interactive geometry local editing method is developed. The method deforms the sample points in a region of interest by manipulating handle points. In the preprocessing step, a non-local denoising algorithm is applied to smooth the input noisy point-sampled model and as a postprocessing step, a new up-sampling and relaxation procedure is proposed to refine the deformed model. The effectiveness of the proposed method is demonstrated by examples, i.e., the editing operation can deform the model while respecting the intrinsic geometric details.

High quality triangulation of implicit surfaces

We present a new high quality tessellation method for implicit surfaces in this paper. The approach can handle arbitrary implicit functions and dynamic implicit surfaces based on skeletal primitives. We first samples the implicit surface uniformly using particle fission and floating, then reconstructs a triangular mesh from the sample points using ball pivoting algorithm (BPA). Finally, we subdivide the reconstructed surface using a 1 to 4 subdivision scheme to obtain the high quality implicit surface tessellation.

Speed control in path motion

A new method for control of path motion is presented. To describe the motion of an object, we adopt two independent control curves, namely the path of the object in 3D space and the velocity curve of the object along the path in 2D space. Techniques for constructing the velocity curve according to various application are presented. The task of finding the exact position of the object along the path is facilitated by employment of a look-up table which matches the arclength of the path with a corresponding parameter value. An efficient arclength parametrization algorithm for path curve of Bezier form is developed.

Converting triangular Bezier surface into optimal trimmed tensor-product Bezier surface

Triangular Bezier surface is widely used for modelling complex object. However most of geometric modelling systems do not support it. It is necessary to convert it into tensor-product Bezier surface. In this paper, a new conversion algorithm is proposed to convert a triangular Bezier surface into an optimal trimmed tensor-product Bezier surface by using polynomial interpolation. Then the proposed algorithm is compared with previous algorithms in both computational cost and numerical accuracy. The results show that the proposed algorithm has both computational and storage advantages over previous algorithms. Its numerical accuracy is comparable with the previous ones for cases of the degree less than 6.

Explicit formulas for bicubic spline surface interpolation

In this paper, explicit formulas are developed for representing a uniform bicubic spline surface that passes through an array of data points. The interpolated surface in the closed case is topologically equivalent to a torus. Open surface cases are reduced to closed surface cases by introducing one or two rows of `free points such that the spline surface wraps around its boundaries. Ordinary interpolation surfaces in open cases can thus be constructed with the same formulas. It turns to be more intuitive and effective to control and modify the shape of the resultant surfaces by adjusting `free points than by the usual derivatives and twist vectors. The interpolation surface is obtained in a two step way and the procedure is very easy to implement. Experimental results demonstrate that the proposed formulas are practically useful.